A uniform lamina is in the form of a triangle \(OBC\), with \(OC=18a\), \(OB=24a\), and \(\angle COB=90^\circ\). The point \(A\) on \(OB\) is such that \(OA=x\). The triangle \(OAC\) is removed from the lamina.

(a) Find, in terms of \(a\) and \(x\), the distance of the centre of mass of the remaining object \(ABC\) from \(OC\).

The object \(ABC\) is suspended from \(C\). In its equilibrium position, the side \(AB\) makes an angle \(\theta\) with the vertical, where \(\tan\theta=\dfrac65\).

(b) Find \(x\) in terms of \(a\).